Le lundi 2 juillet 2012, à 14h30, dans la salle de conférence de l'OSUR (campus de Beaulieu, RDC du Bât 14B), Pietro de Anna soutient sa thèse intitulée
Le lundi 2 juillet 2012, à 14h30
, dans la salle de conférence de l'OSUR (campus de Beaulieu, RDC du Bât 14B), Pietro de Anna soutient sa thèse intituléeMixing and reactions in porous medial
Le jury est composé de :Tanguy Le Borgne
(Rennes, co-directeur de thèse),Philippe Davy
(Rennes, directeur de thèse),Yves Meheust
(Rennes, examinateur),Renaud Delannay
(président / Rennes)Emmanuel Villermaux
(Marseille, rapporteur)Philippe Ackerer
(Strasbourg, rapporteur)Aldo Fiori
(Rome, Italie, examinateur)Jesus Carrera
(Barcelone, Espagne, examinateur)Résumé
In this thesis we use a stochastic approach to address the upscaling of mixing dominated reactions in flows thorough heterogeneous porous media. For the case where the transport is represented only by diffusion, fluctuations in spatial concentration distribution lead to segregation of chemicals and thus to anomalous kinetics. We show that the transition from the expected behavior shown by well mixed systems to this anomalous kinetics is intimately linked to the evolution of the concentration PDF from a Gaussian to non-Gaussian shape. This fact establishes a direct relationship between anomalous reaction kinetics, incomplete mixing and the non-Gaussian nature of the concentration PDF.
Introducing advective transport processes in our analysis, we studied the impact of incomplete mixing on effective reaction kinetics at the front between two solutes, one displacing the other, in a 2d heterogeneous porous medium. While classical Fickian models predict a scaling for the mass production as t^0.5, we show that the kinetics follow 2 non-Fickian regimes. An early times the invading reactant is organized in fingers and the mass production scales as t^2. For later times the mass production slows down, but it is still faster then the t^2 . It does not depends on diffusion and is totally controlled by advective spreading. In this regime, anomalous kinetics is directly related to superdiffusive advective spreading. In order to relate the pore scale flow heterogeneity to advective spreading and subsequently to anomalous kinetics, we analyse the distribution and correlation of Lagrangian velocities. We show the existence of long range temporal correlation of Lagrangian accelerations, which are at the root of the breakdown of classical Fickian dispersion models. Thus, similarly to turbulent media, flow through porous media displays strong intermittent properties. We demonstrate that they can be quantified by a correlated Continuous Time Random Walk approach, which provides a consistent upscaling framework.
We finally perform a laboratory experiment where a quasi 2D system is studied through an Hele-Shaw cell in which two reactive chemicals are injected, one displacing the other. A new experimental set up based on chemiluminescence reactions allows high resolution quantification of the pore scale concentration pdf and reaction rate. The anomalous kinetics of the reactive front is observed and is very consistent with our theoretical predictions.Contact OSUR : Pietro de Anna (Géosciences)